Ceiling Leak from Condensation on Vent Pipe

I had a ceiling leak, between the first and second floor, where a vent pipe from an upstairs bathroom exist. I had a plumber in to find the cause of the leak and his diagnosis is that the vent pipe had sufficient condensation on it, to cause an accumulation of water, thus a leak. He suggests that I put an air vent in the ceiling to allow air to flow into the cavity between the rafters and to help keep the area warm and dry. Does this sound right? Is there an alternative to putting a louvered vent into the ceiling? Since the ceiling has been opened, there no longer exists any condensation.

The "vent" pipe I'm speaking of is a plumbing vent, not an room ventilation device. It is between the first and second floor because it is venting from the drain for a shower, on one side and a sink on the other side in the bathroom on second floor above the kitchen.

The plumbing vent is connected to these drains at a union with a 90 degree connection that then is connected to the stack vent pipe the goes up between an interior wall in the bathroom, through the attic above and exits through the roof.

Yes, the condensation is on the vent stack pipe, where the union and 90 degree elbow exist. There are no leaks from any part of the drainage or water supply systems.

Thank you; I see the picture now. I would ask one more question, and that is : is it possible that condensation on that pipe perhaps in the attic is runnig down the pipe until it finds a horizontal surface to drip from? Otherwise, then I have not seen condensation in a ceiling cavity before, I and I now ask other professionals for their opinion about providing ventilation to that space from the room.

The vent stack in the attic area was checked and was free of any condensation. There was no evidence of any leakage where the vent pipe passed through the roof. There may be the possibility that due to the very heavy and deep snow that accumulated on the roof some of it may have entered the stack, but there is no evidence of any leakage anywhere along the path of the stack or ajoining rafters in the ceiling. In fact the only sign of water in the cavity in the ceiling is directly beneath the union and 90 degree connector. The water lines are about one and a half feet away from the union and vent stack, going toward the outer wall of the house. Water marks are visible on the inner side of the sheet rock only in the vicinity of the vent stack, its union and connector.